We propose to classify the power of algorithms by the complexity of the problems that they can be used to solve. Instead of restricting to the problem a particular algorithm was designed to solve explicitly, however, we include problems that, with polynomial overhead, can be solved ‘implicitly’ during the algorithm’s execution. For example, we allow to solve a decision problem by suitably trans...

The fixed-cost Capacitated Multicommodity Network Design (CMND) problem is a well known NP-hard problem. This paper presents a matheuristic algorithm combining Simulated Annealing (SA) metaheuristic and Simplex method for CMND problem. In the proposed algorithm, a binary array is considered as solution representation and the SA algorithm manages open and closed arcs. Several strategies for open...

Computing a maximum weighted stable set in a bipartite graph is considered wellsolved and usually approached with preflow-push, Ford-Fulkerson or network simplex algorithms. We present a combinatorial algorithm for the problem that is not based on flows. Numerical tests suggest that this algorithm performs quite well in practice and is competitive with flow based algorithms especially in the ca...

Capacitated location-allocation problem with stochastic demands is originally formulated as expected value model, chance-constrained programming and dependent-chance programming according to different criteria. For solving these stochastic models efficiently, the network simplex algorithm, stochastic simulation and genetic algorithm are integrated to produce a hybrid intelligent algorithm. Fina...

Bayesian networks are graphical modeling tools that have been proven very powerful in a variety of application contexts. The purpose of this paper is to provide education practitioners with the background and examples needed to understand Bayesian networks and use them to design and implement student models. The student model is the key component of any adaptive tutoring system, as it stores al...

We present a specialized network simplex algorithm for the budget-constrained minimum cost flow problem, which is an extension of the traditional minimum cost flow problem by a second kind of costs associated with each edge, whose total value in a feasible flow is constrained by a given budget B. We present a fully combinatorial description of the algorithm that is based on a novel incorporatio...

Abstract In this paper we have investigated a fuzzy linear programming problem with fuzzy quantities which are LR triangular fuzzy numbers. The given linear programming problem is rearranged according to the satisfactory level of constraints using breaking point method. By considering the constraints, the arranged problem has been investigated for all optimal solutions connected with satisf...

The transshipment problem is one of the central problems in network optimization. There exist several polynomial and strongly polynomial algorithms for solving this problem (see the surveys [7, 1]). Nevertheless, the method of choice in practice still seems to be the network simplex method. In this paper we shall consider the dual network simplex method. We show that some excess scaling algorit...

This paper presents a fast algorithm to optimize both the widths and lengths of power/ground networks under reliability and power dip/ground bounce constraints. The spacesizing which allows the length to change gives more flexibility in solving practical problems. There are two major contributions of this paper. First, we prove that for general topology, a relaxed version of this problem is als...